Theorems · Theorem · real analysis

HasDerivAt.fun_inv

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝕜' : Type u_1} [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {c : 𝕜 → 𝕜'} {c' : 𝕜'},
  HasDerivAt c c' x → c x ≠ 0 → HasDerivAt (fun i => (c i)⁻¹) (-c' / c x ^ 2) x

Eta-expanded form of HasDerivAt.inv

Defined in

Mathlib.Analysis.Calculus.Deriv.Inv

Cited by

0 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra